Abstract
A liquid drop is supposed suspended in an immiscible liquid of equal density that undergoes slow steady shear flow. From a solution of Stokes' creeping motion equations in which the tangential component of normal stress is assumed continuous across the drop surface, the equation giving the drop shape is found approximately, cubes and higher powers of the deformation parameter D I being neglected compared to unity. D I is proportional to the product of the velocity gradient, the drop radius, the suspending liquid's viscosity, and the reciprocal of the interfacial tension. To second order in D I the drop is not ellipsoidal and in Couette flow its angle of maximum extension, measured from the direction of the velocity gradient, exceeds 1 4 π , approaching 1 2 π for viscous drops at larger D I. The results agree qualitatively with previous experimental descriptions of the deformation phenomenon, but quantitative agreement between calculated angles of maximum extension and previously reported measurements is not found. The disagreement may be due to different interpretations of the angle of maximum extension or more probably to impeded transmission of tangential stress at the interface.
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